A pool of 9 semifinalists for a job consists of 7 men and 2 women. Because all are considered equally qualified, the na of two of the semifinalists are drawn, one after the other, at random, to become finalists for the job. (Round your answ to one decimal place.) (a) What is the probability (as a %) that both finalists are women? Let W₁ be the event that a woman is chosen on the first draw, W₂ be the event that a woman is chosen on the second draw, M₁ be the event that a man is chosen on the first draw, and M₂ be the event that a man is chosen the second draw. % and P(W₂ | W₁) = = X %. Then, as percents, P(W₁) = 22.22 P(W₁ W₂) = P(W₂ | W₁) P(W₁) = Hence, the probability that both finalists are women is 11.11 (b) What is the probability (as a %) that both finalists are men? % X %. (c) What is the probability (as a %) that one finalist is a woman and the other is a man? % X%, and thus
A pool of 9 semifinalists for a job consists of 7 men and 2 women. Because all are considered equally qualified, the na of two of the semifinalists are drawn, one after the other, at random, to become finalists for the job. (Round your answ to one decimal place.) (a) What is the probability (as a %) that both finalists are women? Let W₁ be the event that a woman is chosen on the first draw, W₂ be the event that a woman is chosen on the second draw, M₁ be the event that a man is chosen on the first draw, and M₂ be the event that a man is chosen the second draw. % and P(W₂ | W₁) = = X %. Then, as percents, P(W₁) = 22.22 P(W₁ W₂) = P(W₂ | W₁) P(W₁) = Hence, the probability that both finalists are women is 11.11 (b) What is the probability (as a %) that both finalists are men? % X %. (c) What is the probability (as a %) that one finalist is a woman and the other is a man? % X%, and thus
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Transcribed Image Text:A pool of 9 semifinalists for a job consists of 7 men and 2 women. Because all are considered equally qualified, the names
of two of the semifinalists are drawn, one after the other, at random, to become finalists for the job. (Round your answers
to one decimal place.)
(a) What is the probability (as a %) that both finalists are women?
Let W₁ be the event that a woman is chosen on the first draw, W₂ be the event that a woman is chosen on the
second draw, M₁ be the event that a man is chosen on the first draw, and M₂ be the event that a man is chosen on
the second draw.
Then, as percents, P(W₁) = 22.22
P(W₁ W₂) = P(W₂ | W₁) P(W₁)
Hence, the probability that both finalists are women is 11.11
% and P(W₂ | W₁) =
X %.
=
(b) What is the probability (as a %) that both finalists are men?
%
X %.
(c) What is the probability (as a %) that one finalist is a woman and the other is a man?
%
X%, and thus
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